QQ vs KJs: preflop equity

Over all 1,712,304 boards that can follow this deal, QQ finishes with 67.92% of the pot and KJs with 32.08%.

QQ

67.92%

Wins 67.70%, ties 0.42%

KJs

32.08%

Wins 31.88%, ties 0.42%

Equity counts a tie as half a win. Exact over every board.

QQ against KJs: the numbers

Exact preflop results for QQ against KJs, in percent
HandWinsTiesLosesEquity
QQ67.7040.42431.87267.916
KJs31.8720.42467.70432.084

One side is a pocket pair, the other is a suited hand. The pair sits between the other hand's two cards: one is higher and one is lower, so the pair is exposed to the higher card.

That is a clear edge, 67.92% to 32.08%, but KJs still wins often enough that one hand proves nothing. 0.42% of boards are ties, so the equity of each hand is its win rate plus half of that.

Ranked by equity against a random hand, QQ is number 3 of the 169 starting hands and KJs is number 20.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QQ27,823,000174,00013,098,000
KJs13,098,000174,00027,823,000

24 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.

QQ against KJs read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QQ2.1171.4773.1380.472
KJs0.4723.1381.4772.117

The final column gives the least the pot must offer for each unit called for a call to break even at this equity.

Who is ahead on which flops

By flop texture, QQ's equity runs from 63.10% on monotone flops up to 82.74% on low rainbow flops (nine high or lower). QQ stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

QQ against KJs by flop texture, in percent
FlopShare of flopsQQ winsTiesKJs winsQQ equity
Rainbow, ten or higher23.13864.6840.10835.20864.738
Rainbow, nine or lower7.77182.1311.21016.65982.736
Two-tone46.54565.8170.34833.83565.991
Monotone5.21261.8872.41835.69563.096
Paired17.33472.0800.09927.82172.130

A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.

Compared with a random hand

The table below sets each hand against its own random-hand baseline: a change of -12.01 points for QQ, from 79.93%, and -30.49 for KJs, from 62.57%.

QQ and KJs here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QQ, all flops67.91679.925-12.0090.84975
QQ, rainbow, ten or higher64.73879.925-15.1870.80998
QQ, rainbow, nine or lower82.73679.925+2.8111.03517
QQ, two-tone65.99179.925-13.9340.82566
QQ, monotone63.09679.925-16.8290.78944
QQ, paired72.13079.925-7.7950.90247
KJs, all flops32.08462.567-30.4830.51279
KJs, rainbow, ten or higher35.26262.567-27.3050.56359
KJs, rainbow, nine or lower17.26462.567-45.3030.27593
KJs, two-tone34.00962.567-28.5580.54356
KJs, monotone36.90462.567-25.6630.58983
KJs, paired27.87062.567-34.6970.44544

Does a shared suit matter?

Looking only at deals where the hands share a suit, QQ has 68.16%; looking only at deals where they do not, 67.67%. QQ does better with a shared suit, by 0.49 points.

QQ against KJs by suit overlap, in percent
DealsSpecific dealsShare of dealsQQ winsTiesKJs winsQQ equity
Share a suit1250.0067.9300.46431.60668.162
No shared suit1250.0067.4770.38432.13967.669

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 24 are QQ in one seat and KJs in the other (0.0015%); with the seats swapped too, 48 (0.0030%).

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average QQ takes back $135.84 of it, which is $35.84 more than it put in, and KJs takes back $64.16, $35.84 less than it put in.

Out of 1,000 deals you should see around 677 outright wins for QQ, 319 for KJs, and 4 split pots.

The same matchup from the other side

Swap the hands and you get KJs with 32.08% against QQ with 67.92%. We keep one page per matchup, with the better-ranked hand first.

The calculator link fills in QsQh against KdJd, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.

How this was computed

Method: exact enumeration. The 24 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.

Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.

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